The Mechanics of Lung Tissue under High-Frequency Ventilation

Mark A. Lewis, Markus R. Owen
2001 SIAM Journal on Applied Mathematics  
High-frequency ventilation is a radical departure from conventional lung ventilation, with frequencies greater than 2Hz, and volumes per breath much smaller than the anatomical deadspace. Its use has been shown to benefit premature infants and patients with severe respiratory distress, but a vital question concerns ventilator-induced damage to the lung tissue, and a clear protocol for the most effective treatment has not been identified. Mathematical modeling can help in understanding the
more » ... ical effects of lung ventilation, and hence in establishing such a protocol. In this paper we describe the use of homogenization theory to predict the macroscopic behavior of lung tissue based upon the three dimensional microstructure of respiratory regions, making the simplifying assumption that the microstructure is periodic. This approach yields equations for macroscopic air flow, pressure, and tissue deformation, with parameters which can be determined from a specification of the tissue microstructure and its material properties. We are able to include an alternative hypothesis as to the dependence of lung tissue shear viscosity on the frequency of forcing, known as the structural damping hypothesis. We then show how, if we consider isotropic tissue, the parameters determining the macroscopic response of the tissue can be estimated from bulk measurements. Finally, we consider the solutions of the macroscopic system when we consider variations in just one spatial dimension. In particular, we demonstrate that the structural damping hypothesis leads to markedly different solution behavior.
doi:10.1137/s0036139999363652 fatcat:dj4d74dsazeaho6kwn5ou4kxzu